Length and decomposition of the cohomology of the complement to a hyperplane arrangement

Abstract

Let $\mathcal{A}$ be a hyperplane arrangement in ${\mathbb{C}}^n$. We show that the number of decomposition factors as a perverse sheaf of the direct image $R{j}_{\ast }{\mathbb{C}}_U$ of the constant sheaf on the complement $U$ to the arrangement is given by the Poincaré polynomial of the arrangement. Furthermore we describe the composition factors of $R{j}_{\ast }{\mathbb{C}}_U$ as certain local cohomology sheaves and give their multiplicity.

Final corrected version, with more references added, to appear in Proc. AMS

Cited by in corpus (1)

• On the length of perverse sheaves and D-modules